However, in a realistic situation, there are two types of control errors that effects on the time evolution of the closed system;
deterministic noise and stochastic noise.
Deterministic noise acts as a bias or detuning [1]}, [2]}, [3]}, which will not be considered in this paper.
Our interest is the stochastic noise, which occurs on the control Hamiltonian at each time.
It is one of the crucial obstacles to overcome toward achieving quantum advantage
[4]}, [5]}, [6]}, [7]}.
Actually, it is difficult to completely eliminate the stochastic noise on control fields in an experimental setup.
